A calculus problem by Sourabh Jangid

Calculus Level 5

\[ \dfrac{\displaystyle\left \lfloor\lim_{n\to\infty} n\tan (4\pi e n!) \right\rfloor }{2} = \, ? \]

\(\)
Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.

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